The coefficient of determination deals with variation and is a measure of how well any given regression line represents its data. If a regression line passes through every point, all of the variation could be explained. The further the regression line is away from the points, the less can be explained.

You square the correlation coefficient to get the coefficient of determination.

Let's look at Part A as an example. If r = 0.75, then r^2 = 0.5625, which means that approximately 56% of the total variation in y can be explained by the linear relationship between x and y. The other 44% of the total variation in y is unexplained.